21. Use any method to find the point of intersection of the lines \( x=3 \) and \( y=-2 \). The \( x \)-coordinate of the line \( x=3 \) is always 3 . It can have any \( y \)-coordinate. The \( y \)-coordinate of the line \( y=-2 \) is always -2 . It can have any \( x \)-coordinate.

To find the point of intersection of the lines \( x = 3 \) and \( y = -2 \), you can use the following method: 1. **Understand the Equations:** - The equation \( x = 3 \) represents a **vertical line** where the \( x \)-coordinate is always 3, regardless of the \( y \)-coordinate. This means the line passes through all points where \( x = 3 \), such as (3, 0), (3, 1), (3, -2), etc. - The equation \( y = -2 \) represents a **horizontal line** where the \( y \)-coordinate is always -2, regardless of the \( x \)-coordinate. This means the line passes through all points where \( y = -2 \), such as (0, -2), (3, -2), (-1, -2), etc. 2. **Find the Common Point:** - Since \( x = 3 \) must hold true for all points on the vertical line and \( y = -2 \) must hold true for all points on the horizontal line, the point where both conditions are satisfied will be the intersection point. - Substitute \( x = 3 \) into the horizontal line equation \( y = -2 \): \[ y = -2 \] - This gives the point \( (3, -2) \). 3. **Conclusion:** - The **point of intersection** of the lines \( x = 3 \) and \( y = -2 \) is **\( (3, -2) \)**. **Visual Representation:** ``` y | | * | | |----------|----------- | | | * | +------------------------ x ``` In the graph above: - The vertical line \( x = 3 \) is represented by the vertical line passing through \( x = 3 \). - The horizontal line \( y = -2 \) is represented by the horizontal line passing through \( y = -2 \). - The point where they intersect is \( (3, -2) \).